PUMPA - THE SMART LEARNING APP

AI system creates personalised training plan based on your mistakes

Download now on Google PlayConsider the frequency distribution table.

Height (in m) | \(30 - 40\) | \(40 - 50\) | \(50 - 60\) | \(60 - 70\) | \(70 - 80\) |

Number of trees | \(124\) | \(156\) | \(200\) | \(10\) | \(10\) |

The above frequency table shows that the data are grouped in class intervals. This table shows that the number of trees with various heights.

Consider the interval \(50 - 60\). There are \(200\) trees in the heights between \(50 - 60\) metres. In grouped frequency, the individual observations are not available. Thus, we need to determine the value that indicates the particular interval. This value is called a midpoint or class mark. The midpoint can be determined using the formula:

Midpoint \(= \frac{UCL + LCL}{2}\)

Where \(UCL\) is the upper class limit and \(LCL\) is the lower class limit.

Example:

Consider the interval \(40 - 50\). Let us find the midpoint of this interval.

Here, \(UCL = 40\) and \(LCL = 50\)

Midpoint of \(40 - 50\) is \(\frac{40 + 50}{2} =\) \(\frac{90}{2}\) \(= 45\)

Therefore, the midpoint of the interval \(40 - 50\) is \(45\).

The arithmetic mean of a grouped frequency distribution can be determined using any one of the following methods.

- Direct method
- Assumed mean method
- Step deviation method